Theme Song


FRA : Elle me dit

CHN : 她对我说

ENG : She told me

JPN : 彼女は私に言う

FRA : écris une chanson contente

CHN : 写一首欢快的歌

ENG : Write a happy song

JPN : 幸せな歌を書く

FRA : Pas une chanson déprimante

CHN : 而不是悲伤的歌

ENG : Not a depressing song

JPN : 気のめいるような歌ではない

FRA : Une chanson que tout le monde aime

CHN : 一首让所有人都喜欢的歌

ENG : A song that everyone loves

JPN : みんなが大好きな曲

FRA : Elle me dit

CHN : 她对我说

ENG : She told me

JPN : 彼女は私に言う

FRA : Tu deviendras milliardaire

CHN : 你将成为亿万富翁

ENG : You will become a millionaire

JPN : あなたは億万長者になります

FRA : Tu auras de quoi être fier

CHN : 你将为此感到骄傲

ENG : You will be proud

JPN : あなたは誇りに思うでしょう

1 Setting

1.1 SCSS Setup

# install.packages("remotes")
library('BBmisc', 'rmsfuns')
#remotes::install_github("rstudio/sass")
lib('sass')
## sass 
## TRUE
/* https://stackoverflow.com/a/66029010/3806250 */
h1 { color: #002C54; }
h2 { color: #2F496E; }
h3 { color: #375E97; }
h4 { color: #556DAC; }
h5 { color: #92AAC7; }

/* ----------------------------------------------------------------- */
/* https://gist.github.com/himynameisdave/c7a7ed14500d29e58149#file-broken-gradient-animation-less */
.hover01 {
  /* color: #FFD64D; */
  background: linear-gradient(155deg, #EDAE01 0%, #FFEB94 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #EDAE01 20%, #FFEB94 80%);
    }
  }

.hover02 {
  color: #FFD64D;
  background: linear-gradient(155deg, #002C54 0%, #4CB5F5 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #002C54 20%, #4CB5F5 80%);
    }
  }

.hover03 {
  color: #FFD64D;
  background: linear-gradient(155deg, #A10115 0%, #FF3C5C 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #A10115 20%, #FF3C5C 80%);
    }
  }
## https://stackoverflow.com/a/36846793/3806250
options(width = 999)
knitr::opts_chunk$set(class.source = 'hover01', class.output = 'hover02', class.error = 'hover03')



1.2 Setup

if(!suppressPackageStartupMessages(require('BBmisc'))) {
  install.packages('BBmisc', dependencies = TRUE, INSTALL_opts = '--no-lock')
}
suppressPackageStartupMessages(require('BBmisc'))
# suppressPackageStartupMessages(require('rmsfuns'))

## load packages
pkgs <- c('knitr', 'kableExtra', 'tint', 'dygraphs', 
          'devtools','readr', 'lubridate', 'data.table', 'reprex', 
          'feather', 'purrr', 'quantmod', 'tidyquant', 'plotly', 
          'furrr', 'flyingfox', 'tidyr', 'jsonlite', 'MASS', 
          'timetk', 'plyr', 'dplyr', 'stringr', 'magrittr',
          'tdplyr', 'tidyverse', 'memoise', 'htmltools', 
          'formattable', 'rbokeh', 'dash', 'dashCoreComponents', 
          'dashHtmlComponents', 'dtplyr', 'viridis', 'hrbrthemes', 
          ##https://dashr.plotly.com
          'zoo', 'forecast', 'seasonal', 'seasonalview', 'rjson', 
          'rugarch', 'rmgarch', 'mfGARCH', 'sparklyr', 'jcolors', 
          'microbenchmark', 'dendextend', 'lhmetools', 'ggthemr', 
          'stringr', 'pacman', 'profmem', 'ggthemes', 'paletteer', 
          'htmltools', 'echarts4r', 'tsibble', 'fable', 
          'fabletools', 'tsibbledata', 'tibbletime', 'feasts', 
          'fpp3', 'prophet', 'fasster', 'fpp3', 'MASS', 
          'fable.prophet')

# remotes::install_github("robjhyndman/fpp3-package")
# https://tidyverts.github.io/tidy-forecasting-principles/tsibble.html
# https://facebook.github.io/prophet/docs/quick_start.html
# https://github.com/mpiktas/midasr
# https://github.com/onnokleen/mfGARCH
# devtools::install_github("business-science/tibbletime")
# devtools::install_github("DavisVaughan/furrr")

suppressAll(lib(pkgs))
# load_pkg(pkgs)

## Set the timezone but not change the datetime
Sys.setenv(TZ = 'Asia/Tokyo')
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, knitr.table.format = 'html')#, digits.secs = 6)

suppressAll(lib(pkgs))
# load_pkg(pkgs)

## Set the timezone but not change the datetime
Sys.setenv(TZ = 'Asia/Tokyo')
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, knitr.table.format = 'html')#, digits.secs = 6)

## https://stackoverflow.com/questions/39417003/long-vectors-not-supported-yet-abnor-in-rmd-but-not-in-r-script
knitr::opts_chunk$set(message = FALSE, warning = FALSE)#, 
                      #cache = TRUE, cache.lazy = FALSE)

## https://www.researchgate.net/post/How_to_solve_abnor_cannot_allocate_vector_of_size_12_Gb_in_R
#memory.size() ### Checking your memory size
#memory.limit() ## Checking the set limit
#memory.size(size=500000)
#memory.limit(size=56000) ### expanding your memory _ here it goes beyond to your actually memory. This 56000 is proposed for 64Bit.
rm(pkgs)

2 Data

2.1 Read Data

## read files if not exists
if(!exists('dsmp')) {
  
  if(str_detect(Sys.info()[1], 'Linux')) {
    
    ## check if data path set
    if(!exists('.dtr')) {
      .dtr <- '/home/englianhu/Documents/GitHub/binary.com-interview-question-data/'}
    dsmp <- readRDS(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))
    
    ## save files if not exists
    if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))) {
      saveRDS(dsmp, paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))}
    
  }
  
  if(str_detect(Sys.info()[1], 'Windows')) {
    
    ## check if data path set
    if(!exists('.dtr')) {
      .dtr <- 'C:/Users/User/Documents/GitHub/binary.com-interview-question-data/'}
    dsmp <- readRDS(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))
    
    ## save files if not exists
    if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))) {
      saveRDS(dsmp, paste0(.dtr, 'data/fx/USDJPY/dsmp.rds'))}
    
  }
}

dsmp <- dsmp |> 
  ## as_tsibble() when needed since we can set number of keys
  #as_tsibble(key = c(close, quarter, month, week, wkdays), index = index) |> 
  arrange(index)
## plot sample data
rbind(head(dsmp, 3), tail(dsmp, 3)) %>% 
  kbl(caption = '1 min Close Price Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
1 min Close Price Dataset
index year quarter month week wkdays wk_1m dy_1m hr_1m sq date close
2015-01-05 00:01:00 2015 1 1 1 Monday 1 1 1 1 2015-01-05 120.5740
2015-01-05 00:02:00 2015 1 1 1 Monday 2 2 2 2 2015-01-05 120.5900
2015-01-05 00:03:00 2015 1 1 1 Monday 3 3 3 3 2015-01-05 120.6035
2018-07-06 23:58:00 2018 3 7 27 Friday 7198 1438 58 1324798 2018-07-06 110.4740
2018-07-06 23:59:00 2018 3 7 27 Friday 7199 1439 59 1324799 2018-07-06 110.4740
2018-07-07 00:00:00 2018 3 7 27 Saturday 7200 1440 60 1324800 2018-07-07 110.4740

source : 1324800 x 12

2.2 Filter Data

## plot sample data
dp_df <- dsmp[dsmp$index %in% dsmp$index[duplicated(dsmp$index)],]
rbind(head(dp_df, 3), tail(dp_df, 3)) %>% 
  kbl(caption = 'NA and Duplicated Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) %>% ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
NA and Duplicated Dataset
index year quarter month week wkdays wk_1m dy_1m hr_1m sq date close
2018-01-02 00:01:00 2018 1 1 1 Tuesday 2 2 2 1123202 2018-01-02 112.6295
2018-01-02 00:01:00 2017 1 1 53 Tuesday 1 1 1 1123201 2018-01-02 NA
2018-01-02 00:02:00 2018 1 1 1 Tuesday 4 4 4 1123204 2018-01-02 112.6295
2018-01-06 23:59:00 2017 1 1 53 Saturday 7197 1437 57 1137597 2018-01-06 NA
2018-01-07 00:00:00 2018 1 1 1 Sunday 7200 1440 60 1137600 2018-01-07 113.0580
2018-01-07 00:00:00 2017 1 1 53 Sunday 7199 1439 59 1137599 2018-01-07 NA

source : 14400 x 12

from above table, we know there have same index and NA value, here we need to rearrange the durations an sq columns elements.

ddsmp <- na.omit(dsmp) |> 
    {\(df) df |> 
         dplyr::mutate(
             sq = 1:n(), 
             date = as_date(index), 
             quarter = quarter(index), 
             month = month(index), 
             wkdays = weekdays(index), 
             wk_1m = rep(1:7200, nrow(df)/7200), 
             dy_1m = rep(1:1440, nrow(df)/1440), 
             hr_1m = rep(1:60, nrow(df)/60)) |> 
         dplyr::select(index, year, quarter, month, 
                       week, wkdays, wk_1m, dy_1m, hr_1m, 
                       sq, date, close)}()

## save files if not exists
if(!file.exists(paste0(.dtr, 'data/fx/USDJPY/ddsmp.rds'))) {
  saveRDS(ddsmp, paste0(.dtr, 'data/fx/USDJPY/ddsmp.rds'))}

source : 1317600 x 12

## plot sample data
rbind(head(ddsmp, 3), tail(ddsmp, 3)) %>% 
  kbl(caption = '1 min Close Price Dataset', escape = FALSE) %>% 
  row_spec(0, background = 'DimGrey', color = 'gold', bold = TRUE) |> 
  column_spec(1, background = 'CornflowerBlue') |> 
  column_spec(2, background = 'Gray') |> 
  column_spec(3, background = 'DarkGrey') |> 
  column_spec(4, background = 'Gray') |> 
  column_spec(5, background = 'DarkGrey') |> 
  column_spec(6, background = '#4897D8') |> 
  column_spec(7, background = '#556DAC') |> 
  column_spec(8, background = '#92AAC7') |> 
  column_spec(9, background = '#556DAC') |> 
  column_spec(10, background = '#375E97') |> 
  column_spec(11, background = 'CornflowerBlue') |> 
  column_spec(12, background = 'LightGray', color = 'goldenrod') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  kable_material(full_width = FALSE) |> ##`full_width = FALSE` will auto adjust every single columns width to fit the table full width.
  scroll_box(width = '100%', fixed_thead = TRUE, height = '400px')
1 min Close Price Dataset
index year quarter month week wkdays wk_1m dy_1m hr_1m sq date close
2015-01-05 00:01:00 2015 1 1 1 Monday 1 1 1 1 2015-01-05 120.5740
2015-01-05 00:02:00 2015 1 1 1 Monday 2 2 2 2 2015-01-05 120.5900
2015-01-05 00:03:00 2015 1 1 1 Monday 3 3 3 3 2015-01-05 120.6035
2018-07-06 23:58:00 2018 3 7 27 Friday 7198 1438 58 1317598 2018-07-06 110.4740
2018-07-06 23:59:00 2018 3 7 27 Friday 7199 1439 59 1317599 2018-07-06 110.4740
2018-07-07 00:00:00 2018 3 7 27 Saturday 7200 1440 60 1317600 2018-07-07 110.4740

source : 1317600 x 12

3 Modeling

3.1 Seasonal Modelling

## convert to time series tsibble
ts1_ddsmp <- as_tsibble(ddsmp, index = index)

ts2_ddsmp <- ddsmp |> 
  as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)

timeID <- unique(ddsmp$date)
bse <- ddsmp[ddsmp$year == 2016,]$date[1] #"2016-01-04" #1st trading date in 2nd year
timeID %<>% .[. >= bse]
#timeID %<>% .[. >= as_date('2016-01-04')]
vrb <- 1200 #1200 observations
frb <- 1
i   <- 1
train1A <- ts1_ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb)}()

fit1A <- train1A |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))

fc1A <- fit1A |> 
  {\(.) forecast(.$close, h = frb)}()
## Error in NROW(new_data): argument "new_data" is missing, with no default
fc1A |> 
  accuracy(ts1_ddsmp)
## Error in accuracy(fc1A, ts1_ddsmp): object 'fc1A' not found
train1B <- ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb) |> 
            as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)}()

fit1B <- train1B |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))
## Error: Input must be a vector, not a function.
fc1B <- fit1B |> 
  {\(.) forecast(.$close, h = frb)}()
## Error in forecast(.$close, h = frb): object 'fit1B' not found
fc1B |> 
  accuracy(ts1_ddsmp)
## Error in accuracy(fc1B, ts1_ddsmp): object 'fc1B' not found
train1C <- ts2_ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb)}()

fit1C <- train1C |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))
## Error: Input must be a vector, not a function.
fc1C <- fit1C |> 
  {\(.) forecast(.$close, h = frb)}()
## Error in forecast(.$close, h = frb): object 'fit1C' not found
fc1C |> 
  accuracy(ts2_ddsmp)
## Error in accuracy(fc1C, ts2_ddsmp): object 'fc1C' not found
train1D <- ts2_ddsmp |> 
    {\(.) filter(., date < timeID[i]) |> 
            tail(vrb) |> 
            as_tsibble(key = c(close, quarter, month, week, wkdays), index = index)}()

fit1D <- train1D |> 
    model(
        ets = ETS(close ~ error('M') + trend('N') + season('N')), 
        ets_bc = ETS(box_cox(close, 0.3) ~ error('A') + trend('N') + season('N')),
        arima = ARIMA(close), 
        rw = RW(close), 
        rw_df = RW(close ~ drift()), 
        naive = NAIVE(close), 
        snaive = SNAIVE(close))
## Error: Input must be a vector, not a function.
fc1D <- fit1D |> 
  {\(.) forecast(.$close, h = frb)}()
## Error in forecast(.$close, h = frb): object 'fit1D' not found
fc1D |> 
  accuracy(ts2_ddsmp)
## Error in accuracy(fc1D, ts2_ddsmp): object 'fc1D' not found
## filter data by date
timeID <- unique(dsmp$date)
bse <- dsmp[year == 2016]$date[1] #"2016-01-04" #1st trading date in 2nd year
## Error in year == 2016: comparison (1) is possible only for atomic and list types
timeID %<>% .[. >= bse]
#timeID %<>% .[. >= as_date('2016-01-04')]
vrb <- 7200 #last 7200 observations DT[(.N - (vrb - 1)):.N]
frb <- 1440

i = 1

train <- dsmp[date < timeID[i]][(.N - (vrb - 1)):.N]
## Error in `<.default`(date, timeID[i]): comparison (3) is possible only for atomic and list types
ctr <- (train[,(sq)][1]):(train[.N,(sq)] + frb)
## Error in eval(expr, envir, enclos): object 'train' not found
## convert to tsibble data
train %<>% 
  as_tsibble(key = close, index = index)
## Error in as_tsibble(., key = close, index = index): object 'train' not found
train_test <- dsmp[sq %in% ctr] |> 
  as_tsibble(key = close, index = index)
## Error in sq %in% ctr: object 'sq' not found
## modeling
fit <- train |> 
  model(
    ets = ETS(close), 
    #ets_bc = ETS(box_cox(close, 0.3)),
    arima = ARIMA(close), 
    rw = RW(close), 
    rw_df = RW(close ~ drift()), 
    naive = NAIVE(close), 
    snaive = SNAIVE(close)
    )
## Error in model(train, ets = ETS(close), arima = ARIMA(close), rw = RW(close), : object 'train' not found
## forecast
fc <- fit |> 
  forecast(h = frb)
## Error in forecast(fit, h = frb): object 'fit' not found
## accuracy
fc |> fabletools::accuracy(train_test)
## Error in fabletools::accuracy(fc, train_test): object 'fc' not found

3.2 timetk::tk_ts()

Chapter 12 Advanced forecasting methods in Forecasting: Principles and Practice (3rd Edt)

my_dcmp_spec <- decomposition_model(
  STL(close ~ season(period = 1440), robust = TRUE),
  ETS(season_adjust ~ season('N')))

fit <- smp1 |> 
  as_tsibble(index = index) |> 
  model(
    ets = ETS(close ~ trend('A')), 
    ets_bc = ETS(box_cox(close, 0.3)), #https://stackoverflow.com/questions/26617587/finding-optimal-lambda-for-box-cox-transform-in-r
    #ets_lg = ETS(my_scaled_logit(mdeaths, 750, 3000) ~ error('A') + trend('N') + season('A')), #http://fable.tidyverts.org/articles/transformations.html
    arima = ARIMA(close), 
    rw = RW(close), 
    rw_df = RW(close ~ drift()), 
    naive = NAIVE(close), 
    snaive = SNAIVE(close), 
    snaive_ = SNAIVE(close ~ lag('year'))#,
    #dcmp = my_dcmp_spec
    )
## Error in as_tsibble(smp1, index = index): object 'smp1' not found
fit |>
  forecast(h = 1440) |> 
  autoplot()
## Error in forecast(fit, h = 1440): object 'fit' not found
#dsmp |> as_tsibble(key = c(qrt, mon, wek, wkdays, sq_1m), index = index)

4 Conclusion

4.1 Summary

4.2 Final Conclude

5 Appendix

5.1 Blooper

5.2 Documenting File Creation

  • File creation date: 2018-08-28
  • File latest updated date: 2021-06-07
  • R version 4.1.0 (2021-05-18)
  • R version (short form): 4.1.0
  • rmarkdown package version: 2.8
  • File version: 1.0.1
  • Author Profile: ®γσ, Eng Lian Hu
  • GitHub: Source Code
  • Additional session information:
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('magrittr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))
suppressMessages(require('knitr', quietly = TRUE))
suppressMessages(require('kableExtra', quietly = TRUE))

sys1 <- devtools::session_info()$platform %>% 
    unlist() %>% 
    (function(df) data.frame(Category = names(df), session_info = df))()
rownames(sys1) <- NULL

sys2 <- data.frame(Sys.info()) |> 
    (function(df) df |> 
         dplyr::mutate(Category = rownames(df)) |> 
         dplyr::select(2,1) |> 
         dplyr::rename('Sys.info' = 'Sys.info..'))()
rownames(sys2) <- NULL

if (nrow(sys1) == 9 & nrow(sys2) == 8) {
  sys2 %<>% rbind(., data.frame(
  Category = 'Current time', 
  Sys.info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
} else {
  sys1 %<>% rbind(., data.frame(
  Category = 'Current time', 
  session_info = paste(as.character(lubridate::now('Asia/Tokyo')), 'JST🗾')))
}

sys <- cbind(sys1, sys2) |> 
  kbl(caption = 'Additional session information:') |> 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) |> 
  row_spec(0, background = 'DimGrey', color = 'yellow') |> 
  column_spec(1, background = 'CornflowerBlue', color = 'red') |> 
  column_spec(2, background = 'grey', color = 'black') |> 
  column_spec(3, background = 'CornflowerBlue', color = 'blue') |> 
  column_spec(4, background = 'grey', color = 'white') |> 
  row_spec(9, bold = T, color = 'yellow', background = '#D7261E')

rm(sys1, sys2)
sys
Additional session information:
Category session_info Category Sys.info
version R version 4.1.0 (2021-05-18) sysname Linux
os Ubuntu 20.04.2 LTS release 5.8.0-55-generic
system x86_64, linux-gnu version #62~20.04.1-Ubuntu SMP Wed Jun 2 08:55:04 UTC 2021
ui X11 nodename Scibrokes-Trading
language en machine x86_64
collate en_US.UTF-8 login englianhu
ctype en_US.UTF-8 user englianhu
tz Asia/Tokyo effective_user englianhu
date 2021-06-07 Current time 2021-06-07 03:00:13 JST🗾